Is there a way to hide the masking lines when using Texture Paint with masking enabled?
As far as I know there is no such option, which disables the white lines.
In Weight Paint Mode you have an option to display vertices instead of edges, but in Texture Paint Mode there is no option like this.



I think that using the Clipping Border Tool may be a good solution for you. Press ALT+B and drag a mouse to select the portion of the model which you want to be visible.



You can rotate selected portion, and paint on it precisely. And the most important is, there are no lines that may disturb you :).